Theory

Airborne Inertial Navigation Systems (INS) are dead reckoning systems that measure the accelerations of the aircraft relative to the inertial space. Because of this frame of reference, the accelerations must then be corrected to represent accelerations relative to the Earth coordinate system to be output by the navigation system. Further, due to the rotation of the earth about its axis, and a north/south or a vertical velocity of the platform, the measured accelerations include two ‘apparent’ components- the centrifugal accelerations (function of latitude) and the coriolis accelerations (function of latitude, north/south velocity, and vertical velocity). These do not contribute to the motion of the vehicle across the surface of the Earth and hence these accelerations must be computed and subtracted from the total measured acceleration.

All INS systems have the following fundamental components:

  • Accelerometers
  • Gyroscopes
  • Computer

The accelerometers measures the vehicle (aircraft) accelerations in three orthogonal axes, and the gyroscopes maintains the reference level condition of the stable platform, which in turn provides a reference plane. The computer calculates current velocity and position from the measured accelerations, provides correction signals due to the transport rates over the Earth’s surface to bias the gyroscopes to properly stabilize the stable platform, and provides the centrifugal and coriolis corrections to the accelerometer outputs.

There are two basic platform stabilization techniques. These are the north-pointing and wander azimuth systems. The north-pointing system maintains a reference axis on the stable platform aligned with true north at all times while the wander azimuth system allows the reference axis to assume an arbitrary, continuously changing angle relative to true north. The north-pointing system must apply correction torques to the gyros as it translates across the earth’s surface to maintain the proper alignment of the reference axis, while the wander azimuth system must continuously compute the wander azimuth angle to resolve the measured accelerations into north/south and east/west components.

The stable platform can also be designed to maintain its orientation with respect to the earth and inertial space in one of the following ways:

  • Analytic. The gyroscopes and accelerometers are oriented to a fixed reference point in inertial space.
  • Semi-Analytic. The gyroscopes and accelerometers are oriented to local vertical at the present latitude and longitude (perpendicular to the earth’s gravitational force).
  • Geometric. The gyroscopes are oriented in inertial space and the accelerometers are oriented to local vertical.
  • Strap-Down. The gyroscopes do not maintain any set orientation and the accelerometers follow orientation of the vehicle.

Schuler Tuning. Modern local vertical tracking INS systems are designed with Schuler tuning to eliminate errors in the orientation of the stable platform due to acceleration and motion across the surface of the earth. The correct orientation of a semi-analytic system is to maintain the vertical axis of the stable platform with the local vertical at that latitude and longitude. If this orientation is not maintained, the horizontal accelerometers will sense an acceleration due to the force resisting the gravitational pull of the earth and incorrectly compute a horizontal velocity and horizontal displacement of the platform. This incorrect horizontal displacement would result in an error in true position which would be bounded by the local vertical tracking mechanism and would oscillate with a period of 84.4 min, equivalent to the period of an earth radius pendulum. This oscillation has become known as the Schuler cycle.

Testing

INS testing should include testing throughout an aircraft’s airspeed, attitude, altitude, and mission segments to ensure compatibility.

1. Preflight and alignment are two major steps in the INS’s ability to perform its functions. Without proper initial validation the operators could be falsely led to believe that the system is functioning correctly. The major items checked during preflight and alignment are the warm-up and leveling times, alignment time and accuracy, selfcalibration, build-in-test, controls and displays, response to transients (external to internal power sources, generator checks, mode changes, etc), and other system interfaces. Initial
testing can be done in a laboratory, but ground tests in the actual platform must also be performed. All types of alignments (e.g., normal, fast, inflight) should be examined, and ground testing (drift runs) should be done after the alignments to evaluate the accuracy of the system after performing each type of alignment. Flight testing must be done to validate the test results obtained during laboratory testing and ground testing. Since the accuracy of an alignment may depend on the amount of earth rate present during the
alignment process, the alignment testing should be done at various latitudes, including equatorial and high polar latitudes, and in both the Northern and Southern hemispheres.

The pre-flight and alignment procedures for an INS must enable the operator to ensure system preparation and start-up in a timely, accurate, and concise manner.

The tester should time the pre-flight and alignment procedures for total time required (including the time required for each individual portion). System response to inputs and indications as to status should be examined. The location and accessibility of controls and displays should be reviewed. Many of the cockpit evaluation questions should be re-examined with respect to the INS system. Built-in-Test operation should be reviewed as to time of occurrence, type of readouts provided, and fault display utility. The accuracy and clarity of fault indications and the effects of failures on system operation and accuracy are details that should also be considered.

2.Static Position Accuracy

Once a “navigate” mode has been selected, the INS must in fact navigate to maintain a static position with respect to the earth. Therefore, the accuracy of an INS during a static drift test reveals pertinent information about the accuracy of the alignment and the ability of the system to compensate for earth rotation, centrifugal accelerations, vibration, and the effects of wind and crew motion on the platform.

The operator should perform a normal preflight and alignment of the INS. Upon completion and entry in a normal navigation mode, the aircraft position should be recorded at 5 min intervals. The test should run a minimum of three hours through at least two complete Schuler cycles. Aircraft location and weather conditions should be noted. Position errors in latitude and longitude should be computed and converted to errors in units of nautical miles. The computed errors can then be plotted as a function of time to determine the drift rates. Statistical operations maybe utilized as required to provide mean INS error with the required confidence level.

3.Non-Manouevring Dynamic Position Accuracy

Apart from the computations required of an inertial system during a static drift test, additional forces act upon the system while it is in motion, and these forces require additional computations by the INS. They are coriolis accelerations and changes in the centrifugal accelerations. The system must therefore accurately recognize changes in aircraft heading and attitude to constantly dead reckon the current aircraft position. The inaccurate resolution of accelerations into north/south and east/west components will lead to position errors which will lead to further inaccuracies in the resolution of the measured accelerations which will lead to further position errors. Therefore, position errors tend to compound and accumulate as a function of time. The ability of the INS to minimize this cumulative error is demonstrated by its accuracy in computing current aircraft position during a non-manoeuvring flight test. The rates and forces imparted on the airframe in all three axes should be kept to a minimum.

The aircraft should be flown from point-to-point over surveyed way-points (5 min to 10 min apart) at the minimum possible altitude. Low bank angles and rates should be used with constant 1-g flight to establish baseline performance of the INS while in flight. Flight duration should be consistent with the projected mission length for the airplane and weapon system under test. A north/south track should be included to exercise the ability of the system to compute and compensate for coriolis and centrifugal accelerations, and an east/west track should be included to exercise the ability of the system to compute and compensate for transport rate and to apply corrections to earth rates and centrifugal calculations. Updates of the INS position should not be performed during the flight test.

The usual data taking procedure is to fly over a surveyed way-point at test altitude and when that point appears to pass under the aircraft, the pilot calls “mark”, the INS position display is frozen at that point, and the data recorded. The computed errors should be plotted as a function of time to determine INS drift rates under non-manoeuvring flight conditions. The appropriate statistical operations should be utilized as required to provide mean INS error with the required confidence level.

Note: Ideally, a flight test at high latitudes (because the meridians converge at the poles) and a transit of the equator and the 0 and 180 deg meridians should be performed to evaluate system and software tolerance of hemisphere shifts.

4.Manoeuvring Dynamic Position Accuracy

The INS must be able to successfully navigate within the manoeuvring limits of its aircraft. Rapid changes in attitude, direction, and airspeed will have an impact on the INS in terms of measured accelerations. The ability of the system to accurately measure and resolve these accelerations into north/south, east/west, and vertical components, to compensate for transport motion across the surface of the earth, and to maintain the stable platform perpendicular to the local vertical will be strongly influenced by the severity of the manoeuvres imposed on the INS by the aircraft. The INS must be able to compensate for the effects of manoeuvres and still maintain an accurate dead reckoning position to facilitate mission success.

The low level navigation data collected over surveyed points in non-manoeuvring dynamic flight testing would establish baseline performance. The duration of the non-manoeuvring portion of this flight would approximate the aircraft’s normal mission transit time. At the conclusion of the non-manoeuvring portion of the flight, the aircraft is manoeuvred through various simulated mission tasks. During the manoeuvring period, position data is taken after each major manoeuvre by marking on top surveyed points. After a mission relatable manoeuvring period, the aircraft is flown on a low level non-manoeuvring route over surveyed check points with navigation data being collected by marking on top of surveyed checkpoints. The return portion of the flight should be of a long enough duration to allow any errors created by the manoeuvres to be manifested as position errors in the INS. After landing, static position data is continued to be taken for 2 hrs at 5 min intervals. At the completion of this test, the airplane true heading is recorded and the INS re-aligned and true heading again recorded for comparison.

Latitude error, longitude error, and radial error can be plotted as a function of time with a notation as to the time that the manoeuvres took place. The error rates can then be categorized as ‘before manoeuvring’, ‘during maneuvering’, and ‘post maneuvering’. In addition, the INS drift rates for the entire flight can be evaluated for mission suitability. Appropriate statistical operations maybe utilized as required to provide mean INS error under manoeuvring conditions with the required confidence level.


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